Add desktop engagement metrics.

chrome/browser/ui/browser_list.h

Index: chrome/browser/ui/browser_list.h
diff --git a/chrome/browser/ui/browser_list.h b/chrome/browser/ui/browser_list.h
index 4270d45b51216304b6cd92636af8e8959ef75655..1e718f5871e9eb6691aab62c91b2d2be25813cf4 100644
--- a/chrome/browser/ui/browser_list.h
+++ b/chrome/browser/ui/browser_list.h
@@ -77,6 +77,9 @@ class BrowserList {
   // allows us to determine what the last active Browser was on each desktop.
   static void SetLastActive(Browser* browser);
 
+  // Notifies the observers when the current active browser becomes not active.
+  static void NotifyBrowserNoLongerActive(Browser* browser);

[Lei Zhang, 2016/08/01 17:29:02]

Do you really need this, or can you infer a given |browser| is no longer active
when SetLastActive() gets called for a different |browser| ?

[gayane -on leave until 09-2017, 2016/08/02 17:13:44]

I need this because when user removes the focus from a browser and doesn't
activate any other instance of a browser (like moving to other application) then
the user session should end.

+
   // Closes all browsers for |profile| across all desktops.
   // TODO(mlerman): Move the Profile Deletion flow to use the overloaded
   // version of this method with a callback, then remove this method.